Next, we define the exponential separation condition, which was introduced and studied in [1]}.

Fix an IFS of similarities \(\lbrace S_i\rbrace _{i\in \mathcal {I}}\) .
Given words \(\sigma ,\tau \in \mathcal {I}^n\) , let
\(d(\sigma ,\tau )={\left\lbrace \begin{array}{ll}|S_\sigma (0)-S_\tau (0)| &: \alpha _\sigma =\alpha _\tau \\\infty &:\text{ otherwise}.\end{array}\right.}\) 
